Exporting bones; transformation of quaternions necessary?
The answer is yes: The quaternions do need to be transformed. If a quaternion represents a rotation around an axis in the source coordinate space, then it's inevitably not going to represent a rotation around the "same" axis in the target coordinate space if it isn't transformed.

As to how to do this in Blender:


Convert the quaternion to an axis/angle representation using the built-in API functions.
Transform the axis using the standard axis conversion functions that are supplied for vectors.
Convert the transformed axis/angle back to a quaternion using the built-in API functions.